org.tinfour.common

Class Thresholds

java.lang.Object

org.tinfour.common.Thresholds

public class Thresholds
extends Object

Provides a standard calculation of threshold values appropriate for use in an incremental TIN implementation based on nominal point spacing. With the exception of vertex tolerance, all thresholds are computed using a small multiplier times the Unit of Least Precision (ULP) computed from the nominal point spacing. The vertex tolerance is a fixed fraction of the nominal point spacing.

Field Summary

Fields

Modifier and Type	Field and Description
static double	DELAUNAY_THRESHOLD_FACTOR Factor for computing the Delaunay threshold.
static double	HALF_PLANE_THRESHOLD_FACTOR Factor for computing the half-plane threshold.
static double	IN_CIRCLE_THRESHOLD_FACTOR Factor for computing the in-circle threshold.
static double	PRECISION_THRESHOLD_FACTOR Factor for computing precision threshold.
static double	VERTEX_TOLERANCE_FACTOR_DEFAULT Factor for computing the vertex tolerance.

Constructor Summary

Constructors

Constructor and Description
Thresholds() Constructs thresholds for a nominal point spacing of 1.
Thresholds(double nominalPointSpacing) Constructs threshold values for the specified nominalPointSpacing.

Method Summary

Modifier and Type	Method and Description
double	getCircumcircleDeterminantThreshold() Gets a threshold value giving guidelines for the smallest absolute value result that can be trusted in geometric calculations for for computing a determinant to be used in determining a set of circumcircle center coordinates and radius.
double	getDelaunayThreshold() Gets the computed value for evaluating whether a triangle pair is within sufficient tolerance when testing to see if they approximately meet the Delaunay criterion using the in-circle calculation.
double	getHalfPlaneThreshold() Gets a threshold value giving guidelines for the smallest absolute value result that can be trusted in geometric calculations for determining on which side of a point a plane lies (the "half-plane calculation").
double	getInCircleThreshold() Gets the threshold value indicating when an extended-precision calculation must be used for the in-circle determination.
double	getNominalPointSpacing() Gets the nominal point spacing value specified in the constructor.
double	getPrecisionThreshold() Get a threshold value giving guidelines for the smallest absolute value result from a geometric calculations that can be accepted without concern for an excessive loss of precision.
double	getVertexTolerance() Gets a threshold value indicating the distance at which a pair of (x,y) coordinates will be treated as effectively a match for a vertex.
double	getVertexTolerance2() Gets a threshold value indicating the square of the distance at which a pair of (x,y) coordinates will be treated as effectively a match for a vertex.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

PRECISION_THRESHOLD_FACTOR

public static final double PRECISION_THRESHOLD_FACTOR

Factor for computing precision threshold.

See Also:

Constant Field Values

HALF_PLANE_THRESHOLD_FACTOR

public static final double HALF_PLANE_THRESHOLD_FACTOR

Factor for computing the half-plane threshold.

See Also:

Constant Field Values

DELAUNAY_THRESHOLD_FACTOR

public static final double DELAUNAY_THRESHOLD_FACTOR

Factor for computing the Delaunay threshold.

See Also:

Constant Field Values

IN_CIRCLE_THRESHOLD_FACTOR

public static final double IN_CIRCLE_THRESHOLD_FACTOR

Factor for computing the in-circle threshold.

See Also:

Constant Field Values

VERTEX_TOLERANCE_FACTOR_DEFAULT

public static final double VERTEX_TOLERANCE_FACTOR_DEFAULT

Factor for computing the vertex tolerance.

See Also:

Constant Field Values

Constructor Detail

Thresholds

public Thresholds()

Constructs thresholds for a nominal point spacing of 1.

Thresholds

public Thresholds(double nominalPointSpacing)

Constructs threshold values for the specified nominalPointSpacing. In general, the nominal point spacing is a rough estimate of the mean distance between neighboring points (or vertices). It is used for estimating threshold values for logic used by the IncrementalTin and related classes. A perfect value is not necessary. An estimate within a couple orders of magnitude of the actual value is sufficient.

Parameters:

nominalPointSpacing - a positive, non-zero value

Method Detail

getInCircleThreshold

public double getInCircleThreshold()

Gets the threshold value indicating when an extended-precision calculation must be used for the in-circle determination.

Returns:

a positive value scaled according to the nominal point spacing of the TIN.

getVertexTolerance

public double getVertexTolerance()

Gets a threshold value indicating the distance at which a pair of (x,y) coordinates will be treated as effectively a match for a vertex.

Returns:

a distance in the system of units consistent with the TIN.

getVertexTolerance2

public double getVertexTolerance2()

Gets a threshold value indicating the square of the distance at which a pair of (x,y) coordinates will be treated as effectively a match for a vertex.

Returns:

a distance squared in the system of units consistent with the TIN.

getPrecisionThreshold

public double getPrecisionThreshold()

Get a threshold value giving guidelines for the smallest absolute value result from a geometric calculations that can be accepted without concern for an excessive loss of precision. This value is based on general assumptions about the what constitutes a significant distance given the nominal point spacing of the vertices in the TIN.

Returns:

a small, positive value.

getNominalPointSpacing

public double getNominalPointSpacing()

Gets the nominal point spacing value specified in the constructor. In general, this value is a rough estimate of the mean distance between neighboring points (or vertices).

Returns:

a positive, non-zero value.

getDelaunayThreshold

public double getDelaunayThreshold()

Gets the computed value for evaluating whether a triangle pair is within sufficient tolerance when testing to see if they approximately meet the Delaunay criterion using the in-circle calculation. A positive (non-zero) in-circle value indicates that the pair violates the criterion, but for case where floating-point limitations may result in conflicts, a very small positive value may be acceptable for approximation purposes.

This value is primarily used in test procedures that evaluate the correctness of a TIN constructed by the IncrementalTin class.

Returns:

A positive value much smaller than the nominal point spacing.

getHalfPlaneThreshold

public double getHalfPlaneThreshold()

Gets a threshold value giving guidelines for the smallest absolute value result that can be trusted in geometric calculations for determining on which side of a point a plane lies (the "half-plane calculation"). If the absolute value of the result is smaller than this threshold, extended-precision arithmetic is advised.

Returns:

a positive, non-zero value much smaller than the nominal point spacing.

getCircumcircleDeterminantThreshold

public double getCircumcircleDeterminantThreshold()

Gets a threshold value giving guidelines for the smallest absolute value result that can be trusted in geometric calculations for for computing a determinant to be used in determining a set of circumcircle center coordinates and radius. If the absolute value of the determinant result is smaller than this threshold, extended-precision arithmetic is advised.

Returns:

a positive, non-zero value significantly smaller than the nominal point spacing.